Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms
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We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the iterates via minimization problems with uniformly convex penalty term. The penalty term is allowed to be non-smooth to include L1 and total variation (TV) like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and discontinuities in practical applications. We present the detailed convergence analysis and obtain the regularization property...[Show more]
dc.contributor.author | Jin, Qinian | |
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dc.contributor.author | Zhong, Min | |
dc.date.accessioned | 2015-12-08T22:10:43Z | |
dc.date.available | 2015-12-08T22:10:43Z | |
dc.identifier.issn | 0029-599X | |
dc.identifier.uri | http://hdl.handle.net/1885/29467 | |
dc.description.abstract | We consider the nonstationary iterated Tikhonov regularization in Banach spaces which defines the iterates via minimization problems with uniformly convex penalty term. The penalty term is allowed to be non-smooth to include L1 and total variation (TV) like penalty functionals, which are significant in reconstructing special features of solutions such as sparsity and discontinuities in practical applications. We present the detailed convergence analysis and obtain the regularization property when the method is terminated by the discrepancy principle. In particular we establish the strong convergence and the convergence in Bregman distance which sharply contrast with the known results that only provide weak convergence for a subsequence of the iterative solutions. Some numerical experiments on linear integral equations of first kind and parameter identification in differential equations are reported. | |
dc.publisher | Springer | |
dc.source | Numerische Mathematik | |
dc.title | Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 127 | |
dc.date.issued | 2014 | |
local.identifier.absfor | 010301 - Numerical Analysis | |
local.identifier.ariespublication | u5328909xPUB65 | |
local.type.status | Published Version | |
local.contributor.affiliation | Jin, Qinian, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Zhong, Min, Fudan University | |
local.bibliographicCitation.startpage | 485 | |
local.bibliographicCitation.lastpage | 513 | |
local.identifier.doi | 10.1007/s00211-013-0594-9 | |
local.identifier.absseo | 970101 - Expanding Knowledge in the Mathematical Sciences | |
dc.date.updated | 2015-12-08T07:34:40Z | |
local.identifier.scopusID | 2-s2.0-84902344045 | |
local.identifier.thomsonID | 000337289300004 | |
Collections | ANU Research Publications |
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